Problem $(48$ Points$)$

A system consisting of $1$ kg of $H_{2}O$ undergoes a heat pump cycle composed of the following processes:

Process $1-2$: Constant volume heating from $P_1=\frac{5}{b}ar,T_1=160C$ to $P_2=\frac{10}{b}ar$

Process $2-3$: Constant pressure cooling to saturated vapor

Process $3-4$: Constant volume cooling to $T_4=160C,v_4=0\mathrm{.}194\frac{m^3}{k}g,u_4=1869k\frac{J}{k}g$

Process $4-1$: Isothermal expansion with $Q_{41}=815\mathrm{.}8kJ$

a$)$ For state $1v_1{?}_{?}=0\mathrm{.}3835\frac{m^3}{k}g$ and $u_1{?}_{?}=2575\mathrm{.}2k\frac{J}{k}g.$ Determine state region for state $1.$

b$)$ At state $2$ determine the state re

Problem $(48$ Points$)$

A system consisting of $1$ kg of $H_{2}O$ undergoes a heat pump cycle composed of the following processes:

Process $1-2$: Constant volume heating from $P_1=5$ bar, $T_1=160C$ to $P_2=\frac{10}{b}ar$

Process $2-3$: Constant pressure cooling to saturated vapor

Process $3-4$: Constant volume cooling to $T_4=160C,v_4=0\mathrm{.}194\frac{m^3}{k}g,u_4=1869k\frac{J}{k}g$

Process $4-1$: Isothermal expansion with $Q_{41}=815\mathrm{.}8kJ$

Sat liquid $/$iphase region $x-3$

b$)$ At state $2$ determine the state region, the internal energy, and the specific volume.

$?$

$V=m(P_2-P_1)V_1$

$U=m(P_2-P_1)+U_1$

$\{\begin{array}{c}\text{:}u=\end{array}$

$5$

$($:$u=1(5-10)+2575\mathrm{.}2=262,2\frac{(kJ)}{(kg)}$